Suppose that maria has 150 coins consisting of pennies, nickels, and dimes. the number of nickels she has is 14 less than twice the number of pennies; the number of dimes she has is 22 less than three times the number of pennies. how many coins of each kind does she have?

Let p, n, d represent the number of pennies, nickels, and dimes respectively. The problem statement tells us

... p + n + d = 150

... 2p - n = 14

... 3p - d = 22

Add these three equations to find the number of pennies.

... (p + n + d) + (2p - n) + (3p - d) = 150 + 14 + 22

... 6p = 186

... p = 31

... n = 2*31 - 14 = 48

... d = 3*31 - 22 = 71

Maria has 31 pennies, 48 nickels, and 71 dimes.